The n-dimensional locally twisted cube(LTQ_(n)) is a newly introduced interconnection network for parallel computing.First, the authors illustrate that there exists deadlock in the minimal routing algorithm.Second,by employing the common virtual network dividing technique,a new routing algorithm is presented,which is proved to be deadlock-free.By exploring the property that one LTQ_(n) consists of one n-1-dimensional hypercube(Q_(n-1)) and one n-1-dimensional 2-twisted cube(Q_(n1,2)),the authors apply the existing adaptive routing strategies for Q_(n-1) and Q_(n-1,2) to induce an adaptive routing scheme for LTQ_(n).So the algorithm can route adaptively in the Q_(n-1)0 or in the Q_(n-1,2)1.